When a person dies without a Will, normally the state in which he resides has written a will for them in the Probate statutes. That will direct where any money is left. Normally, when a person dies without a spouse, the children equally are the beneficiaries. With life insurance, the policy most often has a beneficiary designated that overrides a will or the statute.
When there is no beneficiary named, the life insurance proceeds normally become a probate asset that must be admininstered through the Probate court in the county in which the deceased resided. Each state and county has different probate laws, and you need to find out the rules where the decedent lived. Depending on the size of the policy and the state law, a probate estate may or may not need to be started. Some states have "summary" or shortened provisions that allow assets to be distributed without an official estate opened.
What would routinely be needed is a Probate estate opened and one of the children named as the Administrator of the Estate. Then, the Administrator can contact the life insurance company to obtain the paperwork needed to cash in the policy. Some court forms, some life insurance company forms and a certified death certificate are usually needed to receive the proceed.
The funeral home normally will obtain and provide you with the death certificate. The insurance company will not know the person died. You need to call the life insurance company now just to touch base and find out what they will need. They may not give you much information about the actual policy if you are not the named beneficiary. Often, you need the court appointment in order to get actual information. Also, don't be surprised if the insurance company wants to open an account that they keep and issue checks that allow you to use the money, rather than issue a check. They just don't want to see the money leave their accounts. Hopefully, you can process the life insurance proceeds without an attorney. If you run into problems, be sure to contact a Probate attorney to solve them (especially tax issues). It isn't worth it to try to solve some problems yourself.